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Full text of "Mathematical And Physical Papers - Iii"

ON THE MOTION OF PENDULUMS. 139 and indeed Baily arranged the order of the swings in such a manner as to eliminate the effect of a small progressive change. We may therefore take the ratio of the densities as being that of the pressures, which, as already stated, was nearly that of 30 to 1. Hence the values of //, which would be deduced independently from the different experiments on the supposition that pf and not /jb was independent of the density would all be wrong in nearly the same ratio, which would be nearly that of (\/30 + I)2 to 30. This accounts for the remarkable agreement between theory and experiment as regards the time of vibration, notwithstanding the employment of an erroneous law as to the relation between p and p in making the correction for the residual air at the low pressure. Moreover, in order to arrive at the value of /<& which would have been deduced from the experiments on the time of vibration had they been reduced according to Maxwell's law, we have merely to increase the value as obtained in this paper in a ratio which is nearly that given above, or 1 to 1*398. The mean high and low pressures for the four l|-inch spheres were 30*062 and 1*177, numbers which would give for the factor 1*558. Of the three pendulums in the table on p. 79, from which the adopted value of tjfjt! was deduced, the first is the only one for which the pressures are recorded in Baily's paper, and the calculated factor for it is 1*437. The results of the most recent and trustworthy experiments for the determination of p for air are brought together by Mr H. Tom-linson in a paper published in the Philosophical Transactions for 1886, p. 767. From the numbers given by him on p. 768 (first line in the table), and on pp. 784, 785, it appears that the true factor should be about 1*700. It is vV* that enters into the expression for the time of vibration, and the difference between the square roots of 1*7 and 1*4 is only *0925 of the former; and it is only a portion of the correction for inertia in which the viscosity is involved at all. Thus in the case of the IJ-inch spheres (see p. 86), that part of the correction for the air in which alone the viscosity is involved is little more than the one-seventh of the whole; and a fraction of this again which is barely one-tenth would amount to little more than one per cent, of the whole effect of the air. Considering the uncertainties as to some small corrections, such as that for the effect of the confinement of the